Hölder regularity for solutions to complex Monge–Ampère equations
Volume 113 / 2015
Annales Polonici Mathematici 113 (2015), 109-127
MSC: Primary 32W20, 32U15; Secondary 35J96.
DOI: 10.4064/ap113-2-1
Abstract
We consider the Dirichlet problem for the complex Monge–Ampère equation in a bounded strongly hyperconvex Lipschitz domain in $\mathbb C^n$. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is $\mathcal {C}^{1,1}$ and the right hand side has a density in $L^p(\varOmega )$ for some $p>1$, and prove the Hölder continuity of the solution.
